Generalized minimax inequalities for set-valued mappings

• Published in: Journal of mathematical analysis and applications Vol. 281; no. 2; pp. 707 - 723
• Main Authors: Li, S.J., Chen, G.Y., Teo, K.L., Yang, X.Q.
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 15.05.2003; Elsevier
• Subjects: Applied sciences; Calculus of variations and optimal control; Exact sciences and technology; Mathematical analysis; Mathematical programming; Mathematics; Maximal point; Minimal point; Minimax inequality; Nonlinear scalarization function; Operational research and scientific management; Operational research. Management science; Operator theory; Sciences and techniques of general use; Set-valued mapping; Minimal point; Maximal point; Minimax inequality; Set-valued mapping; Nonlinear scalarization function; Monotonic function; Minimal and maximal point; Vector space; Mathematical analysis; Topological space; Set valued mapping; Convexity; Hausdorff space; Vector optimization
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/S0022-247X(03)00197-5

In this paper, we study generalized minimax inequalities in a Hausdorff topological vector space, in which the minimization and the maximization of a two-variable set-valued mapping are alternatively taken in the sense of vector optimization. We establish two types of minimax inequalities by employing a nonlinear scalarization function and its strict monotonicity property. Our results are obtained under weaker convexity assumptions than those existing in the literature. Several examples are given to illustrate our results.